A231986 Decimal expansion of the solid angle (in steradians) subtended by a spherical square of one radian side.

9, 2, 7, 6, 8, 9, 4, 7, 5, 3, 2, 2, 3, 1, 3, 6, 4, 0, 7, 9, 5, 6, 1, 3, 2, 3, 8, 1, 4, 5, 9, 5, 4, 9, 1, 7, 6, 3, 0, 4, 0, 4, 0, 0, 6, 4, 2, 4, 5, 7, 4, 3, 4, 0, 8, 9, 9, 9, 8, 6, 9, 0, 4, 6, 6, 9, 1, 7, 4, 8, 6, 1, 8, 8, 5, 9, 1, 4, 5, 1, 8, 8, 9, 3, 9, 3, 7, 1, 3, 1, 0, 9, 9, 0, 3, 1, 9, 1, 2, 3, 5, 3, 9, 4, 4

Offset: 0

Author

Stanislav Sykora, Nov 17 2013

Keywords

• nonn
• cons
• easy

Comments

In spherical geometry, the solid angle (in steradians) covered by a rectangle with arc-length sides r and s (in radians) equals Omega = 4*arcsin(sin(s/2)*sin(r/2)). For this constant, r = s = 1.

Note: It is a common mistake to think that 1 radian squared gives one steradian! See also the discussion in A231984.

Examples

			0.9276894753223136407956132381459549176304040064245743408999869...
		

References

• G. V. Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, 2012, ISBN 978-0691148922.

Links

• Stanislav Sykora, Table of n, a(n) for n = 0..2000
• Wikipedia, Solid angle, Section 3.3 (Pyramid).
• Wikipedia, Steradian.

Crossrefs

Cf. A072097 (rad/deg), A019685 (deg/rad), A231981 (sr/deg^2), A231982 (deg^2/sr), A231984, A231987 (inverse problem).

Programs

Mathematica

RealDigits[4 * ArcSin[Sin[1/2]^2], 10, 120][[1]] (* Amiram Eldar, May 16 2023 *)

PARI

4*asin(sin(1/2)^2) \\ Charles R Greathouse IV, Feb 07 2025

Formula

Equals 4*arcsin(sin(1/2)^2).